Peter Halley and Alessandro Mendini at Mary Boone Gallery

Peter Halley has been painting pretty much the same ingenious painting for three decades, with evolving minor variations: a hard-edged abstraction of rectangles connected by pipes that results from the careful and repeated application of layers of acrylic, Day-Glo and stucco-like Roll-a-Tex. They’re diagrams of both disciplinary institutions and communications systems—prisons, cells and circuits.

More than three years after his last show at Boone, he returns with nine new canvases in his signature style that are every bit as blazingly hot and electric as the city’s summer weather. They induce the lightheaded pleasures of all-enveloping heat without the concomitant pain, in a pleasantly air-conditioned gallery.

These new paintings look sharper, more exacting, than his previous work. He’s kept their layouts simple—just a cell or two hovering above, and connected to, a short band of ground along the bottom of each. They’re nicely balanced, in deliriously electric palettes of greens (acid and lemon-lime), pinks (bubble-gum and raspberry) and blues (baby, royal and blueberry).

Vaguely cartoonish, even slightly comical, these grids have taken on a new relevance, a horrifying new bite, as more and more of daily life is mediated by and transacted through a proliferating tangle of complex networks. Cassandra-like, he has been prophesying today’s panoptic regime all along.

The works hang atop jazzy gallery-filling wallpaper by the Italian designer Alessandro Mendini, who planned the show with Mr. Halley. The wallpaper is filled with interlocking triangles and rectangles in high-pitched colors—lots of Easter pastels—that are every bit as effervescent as those of the paintings. Spending time in the installation is an immersive experience, like being dropped into a world hatched by the 1980s Italian designers who went under the name Memphis (past Halley collaborators) or being trapped inside a Halley painting. Your eyes rebel at first, then adjust and then beg never to leave.

Is it possible that Mr. Halley’s work will one day look quaint? That’s the safe, if unsettling, bet. The grid ruled the 20th century. In the 21st, more complicated systems are taking hold. Euclidean geometries may end up feeling inadequate to the task of picturing increasingly complex digital structures. For now, though, we can revel in the aesthetic feats of Messrs. Halley and Mendini, bracing ourselves for what is to come.